It is a standard procedure of analysis by magnetic resonance to rotate a sample at a high rate in a uniform field to obtain an improved average homogeneous sample volume. It is also characteristic of certain specific experiments to orient the rotational axis at a selected angle with respect to the polarizing field. In recent years, the employment of pulsed magnetic field gradients has been introduced for purposes such as solvent suppression or for the detection of multi-quantum coherence.
The combination of these arrangements requires an NMR probe which can supply a desired magnetic field gradient over a sample at specified orientation with respect to a uniform magnetic field.
In the prior art, Bowtell and Peters, J. Mag. Res., series 115, pp.55-59 (1995), describe a design for a gradient coil oriented at the "magic angle" comprising wires disposed as contours on the surface of a cylinder axially coincident with a spinning axis and the spinning axis oriented along the polarizing field. This gradient coil is best described as disposed on the planar surface having dimensions extending from -z.sub.0 to +z.sub.0 by -r.phi. to +r.phi. formed by unrolling the cylindrical surface. For the purposes of this work the z direction will be taken as the axis of the cylinder rather than the direction of the polarizing field. The angle .phi. is the azimuthal angle about the periphery of the cylinder. It is important to note that this prior art places the axis of the rotating sample (coincident with the polarizing axis) while the gradient is designed to be directed at the magic angle with respect to the (coincident ) polarizing/rotational axis.
In another example of prior art, a gradient coil is described for disposition on a cylindrical surface oriented at an angle with respect to the polarizing field and producing a gradient having a linear dependence of magnetic field component B.sub.p in the polarizing field direction as a function of displacement along the rotational axis z, while maintaining uniform gradient field in the plane perpendicular to the rotational axis. This is obtained with parallel straight line segments disposed to lie in approximately cylindrical distribution and with appropriately selected currents directed through the several segments. This is described in U.S. Pat. No. 5,872,452 to Cory et al. Note that for this approach currents which would be required to produce a field derived from a theoretical infinitely long cylinder must be adapted to the actual available dimensions of an NMR probe. This truncation, in turn, must be considered for the effect upon the resulting gradient.